SO2Cl2(g) SO2(g) + Cl2(g)
The Kp for the reaction is 2.18 at 648 K. A sample of SO2Cl2 is placed in a container and heated to 648 K while the total pressure is kept constant at 9.00 atm. Calculate the partial pressures of the gases at equilibrium.
To calculate the partial pressures of the gases at equilibrium, we'll use the ideal gas law and the concept of equilibrium.
First, let's assign variables to the partial pressures of the gases at equilibrium. We'll use P(SO2Cl2), P(SO2), and P(Cl2) to represent the partial pressures of SO2Cl2, SO2, and Cl2, respectively.
Since the total pressure is kept constant at 9.00 atm, we can express the partial pressures as the ratios of their individual pressures to the total pressure:
P(SO2Cl2) = x (unknown)
P(SO2) = y (unknown)
P(Cl2) = z (unknown)
Now, we need to use the equilibrium constant, Kp, to set up an equation that relates the partial pressures of the reactants and products. For the given reaction:
SO2Cl2(g) ⇌ SO2(g) + Cl2(g)
The equilibrium expression is:
Kp = (P(SO2) * P(Cl2)) / P(SO2Cl2)
Substituting the given Kp value of 2.18, we have:
2.18 = (y * z) / x (Equation 1)
Since the reaction is at equilibrium and the total pressure is 9.00 atm, we can also write:
P(SO2Cl2) + P(SO2) + P(Cl2) = 9.00
x + y + z = 9.00 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with three unknowns (x, y, and z). To solve the system, we'll use the method of substitution.
Rearrange Equation 2 to solve for x:
x = 9.00 - y - z (Equation 3)
Substitute Equation 3 into Equation 1:
2.18 = (y * z) / (9.00 - y - z)
Multiply both sides of Equation 1 by (9.00 - y - z):
2.18 * (9.00 - y - z) = y * z
Now, we can solve for one variable in terms of the others. However, to simplify the calculation, let's assume y = 1 atm and substitute it into the equation above:
2.18 * (9.00 - 1 - z) = 1 * z
Simplify:
19.78 - 2.18z = z
Move z to the left side:
3.18z = 19.78
Solve for z:
z = 6.21 atm
Now, plug the value of z back into Equation 2 to solve for y:
x + y + z = 9.00
x + 1 + 6.21 = 9.00
x + 7.21 = 9.00
x = 1.79 atm
Finally, substitute the values of x = 1.79 atm and z = 6.21 atm into Equation 2:
1.79 + 1 + 6.21 = 9.00
So, the partial pressures of the gases at equilibrium are approximately:
P(SO2Cl2) = 1.79 atm
P(SO2) = 1 atm
P(Cl2) = 6.21 atm